Ho Pete,

There are better techniques than guess and check but doing the calculations by hand can be horrendous. Even finding the square root of a large number is numerically intensive. In my response to an earlier question from Tom I show how to use the bisection method to approximate the cube root of 270 and then direct Tom to the Newton-Raphson method which for most problems will reach the required accuracy in fewer steps than the bisection method.

Harley